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Ipatiy [6.2K]
3 years ago
13

The coordinate of point T are (3,-11). The midpoint of line ST is (3,-9). Find the coordinates of point S

Mathematics
1 answer:
svetlana [45]3 years ago
5 0

Answer:

(3,-7)

Step-by-step explanation:

Midpoint Formula

(3,-9) = ((3+x)/2 , (-11+x)/2)

Solve for x coordinate

3 =  \frac{3 + x}{2}  \\ 6 = 3 + x \\ 3 = x

Solve for y coordinate

- 9 =  \frac{ - 11 + x}{2}  \\  - 18 =  - 11 + x \\  - 7 = y

Therefore point s is (3, -7)

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Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at a rate of 65
koban [17]

Answer:

time = 1 hour 24 minutes

Step-by-step explanation:

Given that:

Eastbound train travels at a rate of 65 miles per hour

Westbound train travels at a rate of 85 miles per hour

So speed = 65 + 85 = 150 miles per hour

Total distance = 210 miles

We have to find the time

We know that

Distance = time * speed

OR

time = distance / speed

time = 210/150

time = 1.4 hours

Or it can be written as:

time = 1 hour 24 minutes

i hope it will help you!

6 0
3 years ago
At what point does she lose contact with the snowball and fly off at a tangent? That is
postnew [5]

Answer:

α ≥ 48.2°

Step-by-step explanation:

The complete question is given as follows:

" A skier starts at the top of a very large frictionless snowball, with a very small initial speed, and skis straight  down the side. At what point does she lose contact with the snowball and fly off at a tangent? That is, at the  instant she loses contact with the snowball, what angle α does a radial line from the center of the snowball to  the skier make with the vertical?"

- The figure is also attached.

Solution:

- The skier has a mass (m) and the snowball’s radius (r).

- Choose the center of the snowball to be the zero of gravitational  potential. - We can look at the velocity (v) as a function of the angle (α) and find the specific α at which the skier lifts off and  departs from the snowball.

- If we ignore snow-­ski friction along with air resistance, then the one work producing force in this problem, gravity,  is conservative. Therefore the skier’s total mechanical energy at any angle α is the same as her total mechanical  energy at the top of the snowball.

- Hence, From conservation of energy we have:

                       KE (α) + PE(α) = KE(α = 0) + PE(α = 0)

                       0.2*m*v(α)^2 + m*g*r*cos(α) = 0.5*m*[ v(α = 0)]^2 + m*g*r

                       0.2*m*v(α)^2 + m*g*r*cos(α) ≈ m*g*r

                        m*v(α)^2 / r = 2*m*g( 1 - cos(α) )

- The centripetal force (due to gravity) will be mgcosα, so the skier will remain on the snowball as long as gravity  can hold her to that path, i.e. as long as:

                         m*g*cos(α) ≥ 2*m*g( 1 - cos(α) )

- Any radial gravitational force beyond what is necessary for the circular motion will be balanced by the normal  force—or else the skier will sink into the snowball.

- The expression for α_lift becomes:

                            3*cos(α) ≥ 2

                            α ≥ arc cos ( 2/3) ≥ 48.2°

4 0
3 years ago
In parallelogram LMNO, what is the measure of angle M? please helppppp
laiz [17]

Answer:

80 degrees

Step-by-step explanation:

First find the the angles N and L:

5x=3x+40

2x=40

x=20

m<N= 100 m<L=100

Now we know that the sum os all Interior angles of a parallelogram is 360

and you know that opposite sides are equal

hence,

2y= 360-2(100)   y being angle M (or o)

2y= 160

y=80

7 0
2 years ago
Find the exact value of sin ( 7 π 4 ) using reference angles
Firdavs [7]

Answer:

-1/root2

Step-by-step explanation:

7pi/4 radians is the same as -pi/4 radians

sin(-pi/4) is -sin(pi/4) = -1/root2

3 0
3 years ago
What is the surface area of the cylinder d = 10 h = 7
Anna11 [10]
The answer is 120\pi. Hope I helped!
3 0
3 years ago
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